"one step in the manufacture of silicon wafers used in the microelectronics industry is the melt crystallization of silicon into a crystalline silicon ingot. this processis carried out within a special furnace. when the newly solidified ingot is removed from the furnace, it is assumed to have a uniform initial temperature of 1600 k, which is below the crystallization temperature. at this temperature, the thermal conductivity of silicon is 22 w/(m•k), the density is 2300 kg/m3, and the heat capacity is 1000 j/(kg•k). the hot solid silicon ingot is allowed to cool in air maintained at a constant ambient temperature of 30°c. the diameter of the silicon rod is 15 cm. end effects are considered negligible. the convective heat transfer coefficient is 147 w/(m2•k). what temperature will exist 1.5 cm from the surface of the ingot after a cooling time of 583 sec (9.72 min)? " consider the rod as acylinder placed vertically.